I do wish it was a word that had to be completely dropped from marketing/adverting.
For example there is not unlimited storage, hell the visible universe has a storage limit. There is not unlimited upload and download speed, and what if when you start using more space they started exponentially slowing the speed you could access the storage? Unlimited CPU time in processing your request? Unlimited execution slots to process your request? Unlimited queue size when processing your requests.
Hence everything turns into the mess of assumptions.
Yes, indeed, most relevant in this case probably "time" and "bandwidth", put together, even if you saturate the line for a month, they won't throttle you, so for all intents and purposes, the "data cap" is unlimited (or more precise; there is no data cap).
Of course there are practical limits as you can't make your 100Mb/s connection into a gigabit one (ignoring that you can buy burstable in a datacenter, etc, etc).
Where unlimited falls down is when it refers to a endlessly consumable resource, like storage.